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(B) We have $m$ rows and $n$ columns,making a total of $mn$ chairs.We need to seat $m$ students such that no row is vacant. This means each of the $m$

Vedclass · Accepted Answer

$n^m m!$

Vedclass · Answer

(B) We have $m$ rows and $n$ columns,making a total of $mn$ chairs.We need to seat $m$ students such that no row is vacant. This means each of the $m$ rows must contain exactly one student.First,we choose one chair out of $n$ available chairs in each of the $m$ rows. Since there are $n$ choices for each of the $m$ rows,the number of ways to select the chairs is $n 	imes n 	imes \dots 	imes n$ ($m$ times) $= n^m$.Next,the $m$ students can be arranged in these $m$ selected chairs in $m!$ ways.Therefore,the total number of ways is $n^m 	imes m!$.

In an examination hall,there are $mn$ chairs arranged in $m$ rows and $n$ columns. The number of ways in which $m$ students can be seated such that no row is vacant is:

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